Embodiments of the present invention disclosed herein relate to a methodology for estimating statistical distribution characteristics of parameters for product development.
The quality of a semiconductor-device-based product is generally dependent upon design rules and process conditions which are applied to the design and manufacture of the product. With the trend toward further integration of such devices, the design and manufacturing processes of industrial products become increasingly complicated. As a result, it is increasingly difficult to analyze the relationship of product quality relative to the design rules and the process conditions. Therefore, methods are required that can accurately and rapidly analyze correlations between the design rules or the process conditions and the product quality since enhanced accuracy and speed in analysis makes it possible to reduce the time-to-market of a new product.
Specifically, in manufacturing a high-technology semiconductor integrated circuit, the design and manufacturing procedures are quite complicated so that it is difficult to analyze the corresponding correlation. A manufacturer of a semiconductor integrated circuit fabricates the semiconductor integrated circuit based on a specification that defines requirements for electrical and structural characteristics. Early-on in the semiconductor industry, verification of a circuit design in accordance with a specification was performed by a human. However, as semiconductor circuits became more highly integrated, such verification was performed using a computer. Unfortunately, although computers having remarkably excellent computing power are employed for this task, the speed and accuracy of the circuit design verification is remarkably reduced as semiconductor circuit technology becomes more highly integrated.
In addition, as semiconductor devices become further reduced in size, a relative rate of a process variation occurring during the manufacturing process of the semiconductor device becomes increased. That is, a variation rate of process error of design features of the same size with respect to a reference size is further increased in a more highly integrated semiconductor integrated circuit. As a result, it is necessary to consider process variation in the design of the semiconductor integrated circuit. In particular, since the process variation has a great effect on the yield of the semiconductor device, it is increasingly important to estimate variation of the electrical characteristics of the product in accordance with process variation during the design stage.
Specifically, since the electrical characteristics of a semiconductor device are dependent on structural/physical parameters (hereinafter, referred to as independent parameters) such as channel length (L), device width (W), doping profile (Na or Nd), oxide thickness (tox), oxide permittivity (εox), channel length modulation constant (λ), or the like, it is necessary to estimate the statistical distribution of the independent parameters in order to enhance the yield of the semiconductor device. In a conventional method for estimating the statistical distribution of the independent parameters, referring to FIG. 1, a predetermined simulation (S2) is performed to estimate the product characteristic (S3). For simulation, design data, i.e., the independent parameters, are used as input data, wherein it is assumed that the design data have a predetermined distribution characteristic, e.g., a normal distribution characteristic. However, due to complications, such as the process variation or the like, it may not be proper to assume that the input data has the normal distribution characteristic. Since an improper input data incurs an inadequate estimation for product characteristic, it is insufficient that the design data to be used as the input data is assumed to have the normal distribution characteristic. Therefore, it should be necessary to estimate it properly.
Nevertheless, estimation of the statistical distribution of the independent parameters is generally not straightforward. For instance, although it is possible to derive an equation expressing the correlation between the independent parameters and the electrical characteristics dependent thereupon through physical theory, this approach is successful only in a very limited case. That is, in general, the equation may be a multivariable function, and further, variables of the equation are dependent upon process conditions, which are continuously updated for improving the yield of the product. Therefore, in practice, it is quite difficult to derive the equation through a theoretical approach. As a result, it is also difficult to obtain an adequate estimation of statistical distribution of the independent parameters using the conventional method.
In addition, though the statistical distributions of the independent parameters may be obtained from an actual measurement for the independent parameters in principle, it is impossible to measure them, in practice, because the time for measurement is too great. In order to overcome such a technical difficulty, another conventional method of estimating the statistical distribution by modeling one of the independent parameters can be employed. However, this conventional method is still limited in that it cannot extract information about other, non-selected, independent parameters. In particular, since these modeling methods are based on a modeling fitting which requires a long procedure for calculation, they cannot provide a physical meaning for the correlation between the independent parameters and the electrical characteristics dependent thereupon. In addition, a large amount of time is required for such a calculation.